making eye sockets (bird)
I'm not sure if this "precise fit" can be done with sculpting. You could use a boolean modifier and subtract the eye, but that would not create a nice topo mesh.

Can you explain a bit more why it is a problem to ave the eyelid "clip" into the eye slightly. Most people do it that way when modelling eyes because perfect fit sometimes can give render issues like shadows or gaps.
As for the bulging, could you post a close-up of the mesh around the eye? 

cheers,